In operation, the motor of such a fan becomes heated. Due to its position within the casing of the fan, it is difficult to cool the motor. In order to overcome this drawback, it has been proposed to equip the casing with a duct for diverting some of the air within the volute, and more particularly into an upper part of the latter, so as to pass it close to the motor. However, this arrangement is not entirely satisfactory, partly because it does not enable enough air to be diverted, and secondly because it gives rise to high turbulence in the region of the volute into which the inlet end of the diversion duct is open.